Question

Need help with this math problem

Answer 1

Answer:

$f(x)=-5x-3$.

Step-by-step explanation:

From the given machine diagram it is clear that:

$f(x)=-8$ at $x=1$

$f(x)=-13$ at $x=2$

$f(x)=-18$ at $x=3$

It is clear that the value of f(x) decreasing by 5 when the value of x is increasing by 1.

Since the function changing at a constant rate, therefore it represents a linear function.

If a linear function passing through two points, then the equation of line is

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

The given linear function passes through (1,-8) and (2,-13), therefore the linear equation is

$y-(-8)=\dfrac{-13-(-8)}{2-1}(x-1)$

$y+8=\dfrac{-5}{1}(x-1)$

$y+8=-5(x-1)$

$y=-5x+5-8$

$y=-5x-3$

So, the required function is $f(x)=-5x-3$.